A surveying instrument has a rotary encoder for measuring a horizontal angle and a vertical angle (see Patent Document 1 below). As shown in FIG. 1, the rotary encoder includes a dial 1 that rotates along with a telescope. Light from a light source 2 is illuminated onto angular graduations formed as slits 11 along a circumferential direction of the dial 1. Light that has passed through the slits 11 is received by a CCD linear sensor 3. An output of the CCD linear sensor 3 is sent to a CPU (arithmetic control unit) 6 via an A/D converter 5. The CPU 6 determines an angle based on positions (pixel coordinates) of slit images (angular graduation images) on the CCD linear sensor 3 and displays the angle on a display unit 7.
With a conventional rotary encoder used in a surveying instrument, an angle between slits 11 is determined by an interpolation calculation to achieve microscopic angular resolution. To perform the interpolation calculation, calculation is performed by fitting a plurality of successive slit images on the CCD linear sensor 3 to a model that has been determined in advance.
The model used in the interpolation calculation shall now be described. As shown in FIG. 2, in a plane view of the dial 1, R is a distance between a center O of the dial 1 and the CCD linear sensor 3, P0 is a position (pixel number) of a foot of a perpendicular drawn from the center O of the dial 1 to the CCD linear sensor 3, and A0 is an angle at this position P0. Further, Pi is a position (pixel number) of the i-th slit image among the successive slit images and Ai is the angle of the i-th slit image, which is given as a dial graduation. The following formula holds for a triangle PiOP0, and this is used as the model of regression analysis for the interpolation calculation.Pi=R tan(Ai−A0)+P0  (1)    Patent Document 1: Japanese Published Unexamined Patent Application No. 2002-13949